Strength criteria are the basis for rock engineering stability assessment and structural optimization design. To predict the triaxial strength of various lithologies, a novel strength criterion is established based on the ultimate strength. A database consisting of over 1642 triaxial tests conducted on rocks is established to calibrate and validate the criterion. According to the measured and predicted results, the fitting accuracy of the criterion is analyzed and compared with several classical criteria, and the sensitivity of the criterion parameters is further discussed. Results indicate that the criterion exhibits high accuracy in fitting and performs better in sandstone but worse in gneiss. In most samples, the criterion underestimates the triaxial strength, which is beneficial for establishing safety redundancy in engineering. Compared to other classical strength criteria, this particular criterion demonstrates superior fitting accuracy and displays lower sensitivity to parameters that lack physical significance. In addition, a simplified criterion is proposed to predict the strength without triaxial test data. Although its fitting accuracy falls slightly below that of the original criterion, its predictive performance is acceptable. Consistent with the original criterion, the simplified criterion performed significantly better in sandstone than in gneiss, and the simplified criterion also underestimated the strength in most lithologies. Finally, the simplified criterion is applied in the Jinping II hydropower station, and the prediction results confirm its applicability of the simplified criterion on the strength prediction of rocks.